Energy Harvesting Multiple Access Channel with Data Arrivals

We consider the energy harvesting two user Gaussian multiple access channel (MAC), where both of the users harvest energy from nature and their data packets arrive intermittently over time. We find the optimal offline transmit power and rate allocations that maximize the sum rate. First, we show that the optimization problem can be formulated in terms of the data rates only, instead of both transmission powers and data rates. Next, we show that the optimal sum rates are non-decreasing in time, similar to the single-user optimal powers. Then, we use a dual decomposition method to solve this problem efficiently. Specifically, we show that this problem is equivalent to three subproblems where each subproblem is a throughput maximization problem with fading, data and energy arrival constraints. We decompose the problem into inner and outer optimization problems and solve the overall problem using the subgradient descent method. Finally, we consider a relaxed problem where the data and energy arrivals to both of the users are merged into single energy and data queues and show that the optimal sum rates of the original problem are majorized by the solution to this relaxed problem.